Re: How to sample a 2-dim. r.v. with known density function?
- To: mathgroup at smc.vnet.net
- Subject: [mg65280] Re: [mg65247] How to sample a 2-dim. r.v. with known density function?
- From: "Dr A.H. Harker" <a.harker at ucl.ac.uk>
- Date: Thu, 23 Mar 2006 06:58:51 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
Dear Kees, Unless you are really lucky and there is some analytic form you can use, the best bet may be a rejection method. Here you generate pairs from some distribution that is available (if the worst comes to the worst, a scaled uniform distribution) po(x,y) that is everywhere above your desired distribution p(x,y). This means it need not be a normalised distribution (though it must be normalisable). You then accept or reject the point you generate by comparison with p(x,y): for the point (x,y) generate a sample z from a uniform distribution in the range 0 to po(x,y) accept the point if z < p(x,y), otherwise accept it Tony Dr A.H. Harker Department of Physics and Astronomy University College London Gower Street London WC1E 6BT ]->-----Original Message----- ]->From: KvS [mailto:keesvanschaik at gmail.com] To: mathgroup at smc.vnet.net ]->Subject: [mg65280] [mg65247] How to sample a 2-dim. r.v. with known ]->density function? ]-> ]->Hi all, ]-> ]->I guess the title explains it already, I have a 2-dim. ]->density function (the joint density of a geometric Brownian ]->motion with drift and its running maximum to be more ]->precise, explicit formula can e.g. be found ]->here: www.maths.ox.ac.uk/~hambly/PDF/O10/lecture15.pdf) and ]->now I would like to generate random pairs according to this ]->density. I'm not even sure whether a general method for ]->doing this exists, is anybody familiar with a method that I ]->can either implement myself in Mathematica or built-in stuff ]->that can be used to do this? ]-> ]->Lots of thanks in advance, ]-> ]->- Kees ]-> ]-> -- This message has been scanned for viruses and dangerous content by the UCL virus scanning system, and is believed to be clean.